Cheon first proposed a novel algorithm for solving discrete logarithm problem with auxiliary inputs. Given some points , an attacker can solve the secret key efficiently. In this paper, we propose a new algorithm to solve another form of elliptic curve discrete logarithm problem with auxiliary inputs. We show that if some points and a multiplicative cyclic group are given, where is a prime, is the order of . The secret key can be solved in group operations by using storage.